Poster of Workshop.
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Deadline for registration: June 17th 2014
This workshop aims to bring together physicists and mathematicians working in exceptional orthogonal polynomials and related topics.
Exceptional orthogonal polynomials are dense families of orthogonal polynomials that satisfy a Sturm-Liouville problem. They differ from classical polynomials in that their degree sequence contains a finite number of gaps. Darboux transformations are intimately connected with the derivation of such families, and so is the notion of bispectrality and other tools that appear in the theory of integrable systems. In mathematical physics, these functions allow to write exact solutions to rational extensions of classical quantum potentials. From the point of view of special functions and orthogonal polynomials, they are polynomial systems formed by solutions to Fuchsian linear equations that belong to the Heine-Stieltjes class. Similar constructions in the theory of integrable systems allow to construct rational solutions to nonlinear integrable PDEs.
There has been a remarkable activity in the past five years along these lines, and we feel the moment is ripe for a first meeting of many of the researchers who have contributed to this development. The aim of the workshop is to bring together members of several mathematical communities such as: integrable systems, mathematical physics and the theory of orthogonal polynomials, to discuss the overlapping problems that these new developments have posed.